How can i fade a background/object with black border?
I think that the solution for you is in this link: http://wiki.blender.org/index.php/Doc:2.4/Tutorials/Composite_Nodes/Setups/Blur_the_Background
Although I don't know why, but it doesn't work for me. I tried many combinations and ended up with this kind of method (which is experimental). I don't think that this is the proper node setup, but the result is quite fine as you can see below:


Go to Compositing Nodes window and set up the nodes as shown below. Add a Map Value node (Add-->Vector-->Map Value) and experiment with its Offset and Size values.


As I said, I don't think that this is a proper method of doing this, but I wanted to share it with you. It may work for you, but if not, please tell me in comment and I'll delete this answer.